Multiply the following complex numbers: $({-5+5i}) \cdot ({5+2i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5+5i}) \cdot ({5+2i}) = $ $ ({-5} \cdot {5}) + ({-5} \cdot {2}i) + ({5}i \cdot {5}) + ({5}i \cdot {2}i) $ Then simplify the terms: $ (-25) + (-10i) + (25i) + (10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -25 + (-10 + 25)i + 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -25 + (-10 + 25)i - 10 $ The result is simplified: $ (-25 - 10) + (15i) = -35+15i $